Self-aligned spatial frequency doubling

ABSTRACT

In accordance with the invention, there are methods for self-aligned spatial frequency doubling in one dimension and also in two dimension. The method for self-aligned spatial frequency doubling in one dimension can include forming a film stack over a substrate, wherein the film stack comprises a photoresist layer and forming a one-dimensional periodic first pattern having a first pitch p on the photoresist layer using an optical exposure, wherein the first pitch p is at least smaller than twice the bandpass limit for optical exposures. The method can also include forming a second pattern using the first pattern by nonlinear processing steps, wherein the second pattern has a second pitch p 2 =p/2.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 60/824,107 filed on Aug. 31, 2006, the disclosure of which isincorporated by reference herein in its entirety.

FIELD OF THE INVENTION

The present invention relates to optical lithography and moreparticularly to methods for self-aligned spatial frequency doubling anddevices formed by self-aligned spatial frequency doubling.

BACKGROUND OF THE INVENTION

Optical lithography is a well-established technology for the productionof small features on planar substrates. Optical lithography tools arethe mainstay of the integrated circuit industry. The smallest featurepitch that can be produced using a standard optical lithography tool isa grating at a period of λ/2NA where λ is the optical wavelength(typically a 193 nm ArF excimer laser source in current advancedcommercial tools) and NA is the numerical aperture of the exposure tool(currently the highest NA available is about 0.93, higher NA's up to atleast about 1.3 are projected using liquid immersion techniques.) Usingthese parameters, the smallest pitch accessible in a single exposure isabout 74 nm.

Interferometric lithography (IL) is a maskless technique, involving theinterference of a small number of coherent laser beams (often two) thatprovides a simple way to approach optical limits. For IL, the highestavailable NA in air is about 0.98, and the corresponding value in waterimmersion is about 1.41 giving a limiting pitch of about 97 nm in airand about 68 nm with water immersion. Higher index fluids providesanother way for decreasing this pitch; indices of about 1.8 for both theimmersion fluid and the glass prism appear within the realm ofpossibility extending the minimum pitch to about 54 nm.

There are many applications that require even smaller pitch structuresthan are available using these single exposure techniques, and often theeconomics of a particular application precludes the use of the veryexpensive tool set that has been optimized for the integrated circuitindustry. A general technique known as spatial frequency multiplicationhas been introduced to extend the range of optical lithography beyondthese single exposure limits, and is disclosed in U.S. Pat. No.6,042,998 to S. R. J. Brueck and Saleem H. Zaidi, entitled “Method andApparatus for Extending Spatial Frequencies in Photolithography” issuedMar. 28, 2000. The general concept of this invention was to recognizethat the spatial frequency limit discussed above refers to the highestspatial frequency that can be transmitted through an optical system(free-space transmission limit in the case of interferometriclithography without immersion). Various nonlinear processes are readilyavailable in semiconductor processing that can be used to add harmoniccontent to the patterns. A simple example is the use of a high-contrastphotoresist layer that converts a sinusoidal aerial image pattern into asquare wave developed photoresist pattern. Other examples include, butare not limited to, oxygen plasma thinning of photoresist lines andundercutting of patterns during etching. Thus, it is in general possibleto take an aerial image (intensity pattern created by the exposure tool)that in its simplest expression is just:Dose(x)=1+cos(2πx/d+φ)  (1)

where d is the period of the pattern and φ is the phase of the patternwith respect to the origin (x=0), and using these nonlinear functionsconvert the pattern into a structure (for example the photoresistheight) described by a Fourier series:

$\begin{matrix}{{H(x)} = {\sum\limits_{i = 0}^{\infty}{a_{i}{\cos\left( {{2\pi\; i\;{x/d}} + \varphi} \right)}}}} & (2)\end{matrix}$

where the a_(i) are the Fourier coefficients, and in general a_(i)→0 asi→∞. It is clear that the expression in equation 2 has higher frequencycontent (the terms with i>1) than the expression in equation 1. However,all of the terms in equation 1 have the same phase inside the cosinefunction (taken as zero in the expression) and consequently, the densityof the pattern (the number of features per unit length) is fixed.

This limitation was overcome in the previous art by storing the patternin a sacrificial layer, and repeating the process with a phase shift toprint a displaced pattern (essentially interpolation of structures atthe same pitch to produce a pattern at twice the pitch). The simplestcommon example is taking two combs and interlacing the tines. Animportant requirement of this process is alignment between the twolayers, because a slight misalignment in placing the second pattern canresult in a pitch that is not precisely divided in two.

Even though using phase shift masks in conventional lithographic toolsproduces a frequency doubled image of the mask pattern (allowing for themagnification of the optical system) as a result of elimination of thezero-order diffraction, all of the patterns produced in this way arewithin the bandwidth accessible by traditional optical techniques andthis doubling does not constitute an example of extending the densitiesof a pattern beyond those available by standard techniques.

Accordingly, there is a need for new methods for spatial frequencydoubling that provides an inexpensive, large area capability with fewerlithographic steps.

SUMMARY OF THE INVENTION

In accordance with the invention, there is a method for self-alignedspatial frequency doubling in one dimension. The method can includeforming a film stack over a substrate, wherein the film stack caninclude a photoresist layer and forming a one-dimensional periodic firstpattern having a first pitch p on the photoresist layer using an opticalexposure, wherein pitch p is at least smaller than twice the bandpasslimit for optical exposures. The method can also include forming asecond pattern using the first pattern by nonlinear processing steps,wherein the second pattern has a second pitch p₂=p/2.

According to various embodiments, there is a method for self-alignedspatial frequency doubling of a two dimensional pattern. The method caninclude (a) forming a film stack over a substrate, wherein the filmstack can include a photoresist layer, (b) forming a one-dimensionalperiodic first pattern having a first pitch p on the photoresist layerusing an optical exposure, wherein pitch p is at least smaller thantwice the bandpass limit for optical exposures, and (c) forming a secondpattern using the first pattern by nonlinear processing steps, whereinthe second pattern has a second pitch p₂=p/2. The method can furtherinclude repeating the steps a-c to form a third pattern at an angle tothe first pattern, wherein the third pattern can have a pitch of p₃ ofabout p/2.

Additional advantages of the embodiments will be set forth in part inthe description which follows, and in part will be obvious from thedescription, or may be learned by practice of the invention. Theadvantages will be realized and attained by means of the elements andcombinations particularly pointed out in the appended claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the invention, as claimed.

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate embodiments of the invention andtogether with the description, serve to explain the principles of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1D illustrate an exemplary method for self-aligned spatialfrequency doubling, according to various embodiments of the presentteachings.

FIGS. 2A-2H illustrate an exemplary method for self-aligned spatialfrequency doubling of a two dimensional pattern, in accordance with thepresent teachings.

FIGS. 3A-3F illustrate an exemplary method for self-aligned spatialfrequency doubling in one dimension, in accordance with the presentteachings.

FIGS. 4A-4F illustrate another exemplary method for self-aligned spatialfrequency doubling in one dimension, according to various embodiments ofthe present teachings.

FIGS. 5A-5E illustrate an exemplary method for self-aligned spatialfrequency doubling in one dimension, according to various embodiments ofthe present teachings.

FIGS. 6A-6F illustrate another exemplary method for self-aligned spatialfrequency doubling in one dimension, according to various embodiments ofthe present teachings.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to the present embodiments,examples of which are illustrated in the accompanying drawings. Whereverpossible, the same reference numbers will be used throughout thedrawings to refer to the same or like parts.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the invention are approximations, the numericalvalues set forth in the specific examples are reported as precisely aspossible. Any numerical value, however, inherently contains certainerrors necessarily resulting from the standard deviation found in theirrespective testing measurements. Moreover, all ranges disclosed hereinare to be understood to encompass any and all sub-ranges subsumedtherein. For example, a range of “less than 10” can include any and allsub-ranges between (and including) the minimum value of zero and themaximum value of 10, that is, any and all sub-ranges having a minimumvalue of equal to or greater than zero and a maximum value of equal toor less than 10, e.g., 1 to 5. In certain cases, the numerical values asstated for the parameter can take on negative values. In this case, theexample value of range stated as “less that 10” can assume negativevalues, e.g. −1, −2, −3, −10, −20, −30, etc.

According to various embodiments, there is a method for self-alignedspatial frequency doubling in one dimension. The method can includeforming a film stack over a substrate, wherein the film stack includes aphotoresist layer. The method can also include forming a one-dimensionalperiodic first pattern having a first pitch p on the photoresist layerusing an optical exposure, wherein the first pitch p is at least smallerthan twice the bandpass limit for optical exposures. The method canfurther include forming a second pattern using the first pattern bynonlinear processing steps, wherein the second pattern can have a secondpitch p₂=p/2, wherein the second pitch p₂ corresponds to a spatialfrequency that is higher than the spatial frequency corresponding to thebandpass limit of optical exposures. In some embodiments, the secondpattern can be formed in the substrate. In other embodiments, the secondpattern can be formed over the substrate. In various embodiments, themethod can further include transferring the second pattern to thesubstrate.

FIGS. 1A-1E depict an exemplary method for self-aligned spatialfrequency doubling in one dimension. In various embodiments, the step offorming a film stack over a substrate can include forming a protectivelayer 120 over a crystalline substrate 110. In some embodiments, thecrystalline substrate 110 can include silicon (100). In otherembodiments, the crystalline substrate 110 can include gallium arsenide.In various embodiments, the protective layer 120 can include anysuitable metal, such as, for example, chromium and nickel. In someembodiments, the protective layer 120 can include dielectric material,such as, for example, silicon nitride and silicon oxide.

The method can further include forming a one-dimensional periodic firstpattern 125 having a first pitch p on the protective layer 120 using anoptical exposure, wherein the first pitch p is at least smaller thantwice the bandpass limit for optical exposures, as shown in FIG. 1A. Invarious embodiments, the first pattern 125 having a first pitch p can bealong a first direction of the crystalline substrate 110. In someembodiments, the first pattern 125 can be created by photo-lithography.In other embodiments, the pattern 125 can be created usinginterferometric lithography. Yet in some other embodiments, the pattern125 can be created using immersion interferometric lithography. A pitchof about 95 nm can be created using a 193 nm laser source and immersioninterferometric lithography. An apparatus for carrying out immersioninterferometric lithography is described in the U.S. patent applicationSer. No. 11/417,031, the disclosure of which is incorporated byreference herein in its entirety.

The method can also include forming a second pattern 116 using the firstpattern 125 by nonlinear processing steps. The nonlinear processingsteps can include anisotropically etching the crystalline substrate 110to form a second pattern 115 in the crystalline substrate 110, as shownin FIG. 1B. In various embodiments, wherein the crystalline substrate110 includes silicon (100), etching can be carried out using wetetchants, such as, for example, potassium hydroxide. One of ordinaryskill in the art would know that the etch rate of the (100) face ofsilicon can be about 400 times the etch rate of the (111) face ofsilicon at about 80° C. Therefore, if the protective layer 120 isdeposited along the <110> direction of the crystalline substrate 110including silicon (100) and the crystalline substrate 110 is etchedusing potassium hydroxide, V-grooves can be etched into the silicon thatterminate in the low etch rate (111) faces, as shown in FIG. 1B.

The nonlinear processing steps can further include removing theprotective layer 120, as shown in FIG. 1C and anisotropically etchingthe crystalline substrate 110 to form a second pattern 116 in thecrystalline substrate 110 having a pitch of about p/2 along the firstdirection of the crystalline substrate 110, as shown in FIG. 1D. Againfor the crystalline substrate 110 including silicon, the (100) face ofsilicon can etch much faster as compared to that of the alreadyestablished (111) face of silicon, thereby anisotropic etching canresult in a third pattern 116 at twice the spatial frequency of thefirst pattern 125 and the second pattern 115. Thus, starting with afirst pattern 125 on the protective layer 120 having a pitch of about 95nm, a third pattern having the frequency-doubled pitch of about 45 nmcan be created on the crystalline substrate 110 using the exemplarymethod described above. One of ordinary skill in the art would know thata pitch of about 45 nm is well beyond the frequency that can be writtenin the lithographic exposure (limited by transmission medium bandpasseffects to λ/2n=193/2*1.44=67 nm).

FIGS. 2A-2E shows another exemplary method for self-aligned spatialfrequency doubling in one dimension. The method can include forming afilm stack over a substrate 210, wherein the film stack includes aphotoresist (resist) layer 230. In some embodiments, the substrate 210can include an unpatterned silicon wafer. In other embodiments, thesubstrate 210 can include a silicon wafer after some fabrication steps.In various embodiments, the substrate 210 can include a silicon waferhaving one or more layers of silicon oxide, silicon nitride, and otherdielectric material. The method can include forming a one-dimensionalperiodic first pattern 235 having a first pitch p on the resist layer230. In various embodiments, the step of forming a one-dimensionalperiodic first pattern 235 can include forming a first resist pattern235 including a lower first resist layer 232 having a first thickness ofh and a width of about p/4, and a top first resist layer 234 over thelower first resist layer 232, wherein the top first resist layer 234 canhave a second thickness of less than h and a width of about 3p/4,wherein p is a pitch of a lithographic exposure. In various embodiments,the lower first resist layer 232 and the top first resist layer 234 canform a “T” shaped structure. In some embodiments, the first resistpattern 235 can be formed by exposing and developing the top firstresist layer 234 to a desired dimensions and then undercutting the lowerfirst resist layer 232 using a selective isotropic etch process. Invarious embodiments, the first resist layer 230 can include a stackedresist structure wherein the lower first resist layer 232 and the topfirst resist layer 234 can have different dose sensitivities. In variousembodiments, the lower first resist layer 232 can include ananti-reflective coating (ARC) layer and the top first resist layer 234can include a photoresist. In certain embodiments, the lower firstresist layer 232 and the top first resist layer 234 can be an i-linephotoresist. In other embodiments, the lower first resist layer 232 andthe top first resist layer 234 can be a g-line or a deep UV photoresist.Non limiting exemplary photoresist can be “EPIC” resists product seriesmanufactured by Rohm & Haas Electronic Materials (Marlborough, Mass.),“ARF” resist product series manufactured by JSR Micro, Inc. (Sunnyvale,Calif.), and “AX” resist product series manufactured by AZ ElectronicMaterials USA Corp (Charlotte, N.C.). In some embodiments, the firstresist layer 232 can include a bottom anti-reflective coating (BARC) fori-line photoresist. Yet in other embodiments, the first resist layer 232can include a g-line BARC or a deep UV BARC. Non limiting examples ofBARC can be “ARC®” product series, manufactured by Brewer Science, Inc.(Rolla, Mo.), “AR™40A, manufactured by Rohm and Haas (Philadelphia,Pa.), and “ARF” anti-reflective coating product series, manufactured byAZ Electronic Materials USA Corp (Charlotte, N.C.). In an alternativeembodiment, the top layer 234 can be formed with a metal such as, forexample, chromium and nickel or a dielectric such as, for example,silicon dioxide.

The method can also include forming a second pattern 225 using the firstpattern by nonlinear processing steps, as shown in FIGS. 2B-2E. FIGS. 2Band 2C show deposition of a protective layer 220 over the substrate 210under each of a plurality of overhangs of the top first resist layer 234of the first resist layer 230 such that the protective layer 220 forms asecond pattern 225 having a period of p/2. In various embodiments, theprotective layer 220 can include any suitable metal, such as, forexample, chromium and nickel. In some embodiments, the protective layer220 can include dielectric material, such as, for example, siliconnitride and silicon oxide. In some embodiments, the step of depositing aprotective layer 220 over the substrate 210 can include shadowevaporating one or more of a metal layer and a dielectric layer at anangle θ=tan⁻¹(p/4 h). In other embodiments, the step of depositing aprotective layer 220 over the substrate 210 can include depositing theprotective layer 220 over the substrate 210 at a first side of the firstresist layer 230, as shown in FIG. 2B and then depositing the protectivelayer 220 over the substrate 210 at a second side of the first resistlayer 230, as shown in FIG. 2C. The protective layer 220 can bedeposited using any suitable method that can provide line of sightdeposition and also provide narrow angle of arrival of atomic/molecularspecies. Exemplary deposition methods include, but are not limited toe-beam evaporation, filament evaporation, sputter deposition, chemicalvapor deposition, low pressure chemical vapor deposition, and plasmaenhanced chemical vapor deposition. Since, e-beam evaporation is a lowpressure deposition technique and essentially line-of-sight, it is thepreferred technique.

The nonlinear processing steps can also include removing the firstresist layer 230, thereby leaving a second pattern 225 of the protectivelayer 220, as shown in FIG. 2D. In various embodiments, the method canfurther include etching the substrate 210 to transfer the first pattern225 to the substrate 210 thereby forming a patterned layer 215, as shownin FIG. 2E

FIGS. 3A to 3F depict another exemplary method for self-aligned spatialfrequency doubling in one dimension. The method can include providing afilm stack over a substrate, wherein the film stack includes aphotoresist (resist) layer 330 over a sacrificial layer 340. In variousembodiments, the resist 330 can be an i-line photoresist. In otherembodiments, the resist 330 can be a g-line or a deep UV photoresist. Insome embodiments, the sacrificial layer 340 can include polycrystallinesilicon, wherein the crystallite size is small enough so as to not addto line edge roughness in a second pattern 355. In other embodiments,the sacrificial layer 340 can include amorphous silicon. The method canfurther include forming a one-dimensional periodic first pattern 335having a first pitch p on the resist layer 330 using an opticalexposure, as shown in FIG. 3A. In some embodiments, the resist 330 canbe patterned using one or more of photolithography, interferometriclithography, and immersion interferometric lithography. The method canfurther include forming a forming a second pattern 355 using the firstpattern 335 by nonlinear processing steps, wherein the second pattern355 has a second pitch p₂=p/2, as shown in FIGS. 3B-3F. FIG. 3B showsanisotropically etching the sacrificial layer 340 to form a patternedsacrificial layer 345. Any suitable etching process such as, forexample, inductively coupled plasma etching and reactive ion etching canbe used. FIG. 3C shows forming a conformal layer 350 over the patternedsacrificial layer 345, wherein a sidewall thickness of the conformallayer 350 can be about p/4. In various embodiments, the conformal layer350 can be an oxide layer, which both consumes some of the sacrificiallayer 340 and also expands beyond the sacrificial layer 340. In someembodiments, the conformal layer 360 can include dielectric material,such as, for example, PMMA. FIG. 3D shows depositing a polymer layer 360over the conformal layer 350 such that spaces between the conformallayer 350 can be filled. In some embodiments, the polymer layer 360 canbe thicker than the conformal layer 350. In other embodiments, thepolymer layer 360 can be designed to just match the thickness of theconformal layer 350. Any suitable material can be used for thedeposition of the polymer layer 360, including, but not limited topolymethylmethacrylate (PMMA) and benzocyclobutene (BCB) based polymers.Polymer layer 360 can be deposited by conventional techniques, such as,for example, spin coating.

The step of forming a forming a second pattern 355 using the firstpattern 335 by nonlinear processing steps can further include etching aportion of the polymer layer 360 and a top portion of the conformallayer 350 to expose a top portion of the patterned sacrificial layer 345as shown in FIG. 3E. In some embodiments, a low pressure directionaletch can be used to etch back the polymer layer 360 and the conformallayer 350. The nonlinear processing steps can further include removingthe remaining polymer layer 365 and the patterned sacrificial layer 345such that the remaining conformal layer 350 forms a second pattern 355having a pitch of p/2, as shown in FIG. 3F. In some embodiments, theremaining polymer layer 365 can be removed with an appropriate solvent.In other embodiments, the patterned sacrificial layer 345 can bepreferentially etched. For example, the patterned sacrificial layer 345including silicon can be preferentially etched using fluorine containinggases, such as, for example, XeF₂, Fluorine. In some embodiments, theremaining conformal layer 350 can be used to transfer the second pattern355 to the substrate 310. In some embodiments, the method can furtherinclude repeating the process shown in FIGS. 3A-3F to form a twodimensional pattern.

FIGS. 4A to 4F depict another exemplary method for self-aligned spatialfrequency doubling in one dimension. The method can include forming afilm stack over a substrate (not shown). In various embodiments, thestep of forming a film stack can include forming a sacrificial layer 440over an etch stop layer 460 and forming a resist layer 430 over thesacrificial layer 440, as shown in FIG. 4A. The method can furtherinclude forming a one-dimensional periodic first pattern 435 having afirst pitch p on the resist layer 430, as shown in FIG. 4B. The methodcan further include forming a second pattern 455 using the first pattern435 by nonlinear processing steps, as shown in FIGS. 4C-4F, wherein thesecond pattern 455 has a second pitch p₂=p/2. The nonlinear processingsteps can include etching the sacrificial layer 440 to form a patternedsacrificial layer 445, wherein the patterned sacrificial layer 445 has aline width of about p/4, as shown in FIG. 4C. The nonlinear processingsteps can further include forming a conformal layer 450 over thepatterned sacrificial layer 445, wherein a sidewall thickness of theconformal layer 450 can be about p/4, as shown in FIG. 4D. The nonlinearprocessing steps can also include etching a portion of the conformallayer 450 to expose a top surface 442 of the sacrificial layer 440 andto expose a portion of the etch stop layer 460 between the conformallayer 450, as shown in FIG. 4E and removing the patterned sacrificiallayer 445 to form a second pattern 455 having a second pitch of p₂=p/2on the conformal layer 450, as shown in FIG. 4F.

FIGS. 5A-5E illustrate another exemplary method for self-aligned spatialfrequency doubling in one dimension. The method can include forming afilm stack over a substrate 510, wherein the film stack can include alower layer 532 including one or more of an anti-reflective coating anda nitride over a substrate and a top layer 534 including one or more ofa polymer and a photoresist over the lower layer 532. Any suitablepolymer can be used, such as, for example, PMMA and BCB based polymers.Non limiting exemplary photoresist can be “EPIC” resists product seriesmanufactured by Rohm & Haas Electronic Materials (Marlborough, Mass.),“ARF” resist product series manufactured by JSR Micro, Inc. (Sunnyvale,Calif.), and “AX” resist product series manufactured by AZ ElectronicMaterials USA Corp (Charlotte, N.C.). In various embodiments, the lowerlayer 532 can include a g-line BARC or a deep UV BARC. Non limitingexamples of BARC can be “ARC®” product series, manufactured by BrewerScience, Inc. (Rolla, Mo.), “AR™40A, manufactured by Rohm and Haas(Philadelphia, Pa.), and “ARF” anti-reflective coating product series,manufactured by AZ Electronic Materials USA Corp (Charlotte, N.C.).

The method can further include forming a one-dimensional periodic firstpattern 535 having a first pitch p on the film stack as shown in FIG.5A, wherein the one dimensional periodic pattern includes a plurality of“T” structures 530 disposed on the substrate 510. The “T” structure 530can include a lower layer 532 having a first thickness of h and a widthof about p/4, and a top layer 534 over the lower layer 532, wherein thetop layer 534 includes a second thickness of less than h and a width ofabout 3p/4, wherein p is a pitch of a lithographic exposure. The methodcan further include forming a second pattern 525, 515 using the firstpattern 535 by nonlinear processing steps, as shown in FIGS. 5B-5E. Thenonlinear processing steps can include depositing a hard mask material520 vertically over the substrate 510 such that the hard mask material520 forms a first pattern having a period of p, as shown in FIG. 5B. Invarious embodiments, the hard mask material 520 can include any suitablemetal, such as, for example nickel and chromium. In some embodiments,the hard mask material 520 can include any suitable dielectric, such asfor example, silicon oxide and silicon nitride. The nonlinear processingsteps can also include removing the top layer 534 thereby forming asecond pattern 525 having a pitch of p/2, as in FIG. 5C, etching thesubstrate 510 to form the second pattern 515 in the substrate, as inFIG. 5D, and removing the lower layer 532 and the hard mask material520, as shown in FIG. 5E. Any suitable anisotropic etching technique canbe used including, but not limited to inductively coupled plasma andreactive ion etching.

FIGS. 6A-6F illustrate another exemplary method for self-aligned spatialfrequency doubling in one dimension. The method can include forming afilm stack over a substrate, wherein the film stack can include a lowerlayer 632 including one or more of a polymer, a photoresist and adielectric such as for example silicon nitride over a substrate and atop layer 634 including a hard mask material, such as, for example, anoxide or a metal. The method can further include forming aone-dimensional periodic first pattern 635 having a first pitch p on thefilm stack as shown in FIG. 5A, wherein the one dimensional periodicpattern 635 can include a plurality of “T” structures 630 disposed onthe substrate 610. The “T” structure 630 can include a lower layer 632having a first thickness of h and a width of about p/4, and a top layer634 over the lower layer 632, wherein the top layer 634 includes asecond thickness of less than h and a width of about 3p/4, wherein p isa pitch of a lithographic exposure. The method can further includeforming a second pattern 665, 615 using the first pattern 535 bynonlinear processing steps, as shown in FIGS. 6B-5E. The nonlinearprocessing steps can include planarizing the “T” structure 630 with apolymer 660, as shown in FIG. 6B and anisotropically etching the polymer660 through the gaps in the top hard mask layer 634, as in FIG. 6C. Invarious embodiments, the polymer 660 can include any suitable polymer,including, but not limited to, PMMA and BCB based polymers. In variousembodiments, the polymer 660 can be anisotropically etched using one ormore of inductively coupled plasma and reactive ion etching. Thenonlinear processing steps can further include removing the top hardmask layer 634 as shown in FIG. 6D and the lower layer 632 as shown inFIG. 6E, thereby forming a second pattern 665 with the polymer 660having a pitch of p/2. The method for self-aligned spatial frequencydoubling in one dimension can also include etching the substrate 610thereby forming the second pattern 615 having a pitch of p/2 in thesubstrate 610, as shown in FIG. 6F.

According to various embodiments, there is a method for self-alignedspatial frequency doubling of a two dimensional pattern. The method caninclude (a) forming a film stack over a substrate, wherein the filmstack includes a photoresist layer, (b) forming a one-dimensionalperiodic first pattern having a first pitch p on the photoresist layerusing an optical exposure, wherein pitch p₁ is at least smaller thantwice the bandpass limit for optical exposures, and (c) forming a secondpattern using the first pattern by nonlinear processing steps, whereinthe second pattern has a second pitch p₂=p/2. The method can furtherinclude repeating the steps a-c to form a third pattern at an angle tothe first pattern, wherein the third pattern has a pitch of about p/2.In some embodiments, the method can also include transferring the secondpattern of pitch p₂ and the third pattern of pitch p₃ into the filmstack. In other embodiments, the method can include transferring thesecond pattern of pitch p₁ and the third pattern of pitch p₃ into thesubstrate.

An exemplary method for self-aligned spatial frequency doubling of a twodimensional pattern is shown in FIGS. 2A-2H. FIGS. 2A-2E shows a methodfor self-aligned spatial frequency doubling in one dimension, asdescribed earlier. The method for self-aligned spatial frequencydoubling of a two dimensional pattern can include forming a secondresist layer 230′ having a second resist pattern at an angle to thefirst resist pattern 235 over the substrate 210, as shown in FIG. 2F. Insome embodiments, the angle between the first resist pattern and thesecond resist pattern can be 90°. In various embodiments, the secondresist layer 230′ can include a lower second resist layer 232′ having athird thickness of h and a width of about p/4, and a top second resistlayer 234′ over the lower second resist layer 232′, having a fourththickness of less than h and a width of about 3p/4, wherein p is a pitchof a lithographic exposure and said widths are formed as a result of alithographic exposure, development and etch cycle with similarparameters to those used to form the first resist pattern in FIG. 2A.The method can further include depositing one or more of a metal layerand a dielectric layer under each overhang of the top second resistlayer 234′, as shown in FIG. 2G, such that the one or more of a metallayer and a dielectric layer forms a second pattern with a period ofp/2, wherein the second pattern is at an angle to the first pattern 235and removing the second resist layer 230′, as shown in FIG. 2H.

Another exemplary method for forming a two-dimensional pattern caninclude filling the second pattern 116 in the crystalline substrate 110,as shown in FIG. 1D with a planarization material. In variousembodiments, the planarization material can include any suitabledielectric material, such as, for example, silicon oxide, siliconnitride, and sapphire. In other embodiments, the planarization materialcan include any suitable metal. The method can further includeisotropically etching back the planarization material and thecrystalline substrate to expose a second face of the crystallinesubstrate, for example, for silicon (100) as the crystalline substrate110, the face (100) of the silicon an be exposed. The method can furtherinclude repeating the sequence of lithographic exposure and patterndefinition to define a second protective layer with the same pattern asin FIG. 1A, but in the orthogonal direction. Then carrying out the samesequence of etching and removal steps to result in a 2D frequencydoubled pattern. In some embodiments, the method can include flatteninga top surface of the third pattern 116 of the crystalline substrate 110,to provide a new high etch rate surface. Flattening of the top surfacecan be done using any suitable technique, such as, for example, dryetching. An example of a related technique (not involving frequencydoubling but illustrating the capabilities of 2D Si patterning using KOHwet etch processes) is disclosed in: “Nanoscale Two-DimensionalPatterning on Si (001) by Large-Area Intefferometric Lithography andAnisotropic Wet Etching”. S. C. Lee and S. R. J. Brueck, Journal ofVacuum Science and Technology 22, 1949-1952 (2004), the disclosure ofwhich is incorporated by reference herein in its entirety.

Conventional techniques for spatial frequency doubling (and in generalfor spatial frequency multiplication) involve nonlinear processoperations on each exposure to increase the spatial frequency content ofthe resulting pattern from each exposure, and combination of two or moresaid nonlinearly frequency-extended patterns to extend the patterndensity. The object of the present teachings has been to developself-aligned techniques that involve only a single lithographic step fora 1D pattern and only a pair of lithographic steps for a 2D patternfollowed by nonlinear processes that can result in a frequency doubling(or higher multiplicative factor) of the original pattern. Theseprocesses are of use in many applications in which a periodic pattern,at a density beyond that available in a single optical/interferometricexposure is required. Examples include silicon integrated circuits, highdensity patterned storage media and sub-wavelength texturing of opticalmaterials (for example for wire-grid polarizers which typically requirea period ≲λ_(op)/10, where λ_(op) is the operating wavelength of thepolarizer (not the exposure wavelength).

According to various embodiments, there are devices formed by thedisclosed methods. In some embodiments, the devices formed by thedisclosed methods can include, but not limited to gratings, hard diskdrives, liquid crystal panels to align liquid crystals, and variousintegrated circuits. Integrated circuits have historically been themajor driver in the push to finer scale lithography. The industryroadmap, the International Technology Roadmap for Semiconductors (ITRS),www.itrs.net, details both the challenges and the opportunities. Anunderlying premise of the roadmap is that the historical 0.7 shrink/2year cycle, one version of “Moore's Law,” will continue unabated, thejob of the ITRS is to lay out the manufacturing pathway and to identifythe challenges that must be addressed. The first levels of lithographyfor an integrated circuit are typically at the smallest dimensions. Oneof these levels is a transistor gate level, which is typically a 1Dlayout, that is, the smallest dimensions are all in one direction, thegate width, while the length of the gate is typically several timeslonger than this width. Another important level is the contact via level(holes through a dielectric layer to make contact with the gate). Theseare typically in a 2D grid. There are many other emergingdevices/applications for nanoscale lithography. One example is isolateddomains for magnetic storage, there the industry is pushing forextremely small dimensions, as small as ˜10-nm half pitch to continuethe historical trend of density increases in magnetic memory.

While the invention has been illustrated respect to one or moreimplementations, alterations and/or modifications can be made to theillustrated examples without departing from the spirit and scope of theappended claims. In addition, while a particular feature of theinvention may have been disclosed with respect to only one of severalimplementations, such feature may be combined with one or more otherfeatures of the other implementations as may be desired and advantageousfor any given or particular function. Furthermore, to the extent thatthe terms “including”, “includes”, “having”, “has”, “with”, or variantsthereof are used in either the detailed description and the claims, suchterms are intended to be inclusive in a manner similar to the term“comprising.” As used herein, the phrase “X comprises one or more of A,B, and C” means that X can include any of the following: either A, B, orC alone; or combinations of two, such as A and B, B and C, and A and C;or combinations of three A, B and C.

Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope and spiritof the invention being indicated by the following claims.

1. A method for self-aligned spatial frequency doubling in one dimensioncomprising: forming a film stack over a substrate such that the filmstack comprises a first pattern having a first pitch p formed by anoptical exposure, the first pitch p being at least smaller than twicethe bandpass limit for the optical exposure, wherein the formation ofthe first pattern comprises: forming a top resist layer overhanging alower resist layer, the lower resist layer having a thickness of h and awidth of about p/4 and the top resist layer having a thickness of lessthan h and a width of about 3p/4; and forming a second pattern using thefirst pattern by one or more nonlinear processing steps to provide thesecond pattern with a second pitch p₂=p/2; wherein the formation of thesecond pattern comprises: depositing one or more of a metal layer and adielectric layer over the substrate under the overhanging top resistlayer by shadow evaporating at least one of the metal layer or thedielectric layer at an angle θ=tan⁻¹(p/4h) such that the one or more ofthe metal layer and the dielectric layer from the second pattern.
 2. Themethod of claim 1, wherein the second pattern is formed over thesubstrate.
 3. The method of claim 2 further comprising transferring thesecond pattern to the substrate.
 4. The method of claim 1, wherein thestep of forming a film stack over a substrate comprises forming aprotective layer over a crystalline substrate.
 5. The method of claim 4,wherein the first pattern having a first pitch p is along a firstdirection of the crystalline substrate.
 6. The method of claim 4,wherein the step of forming a second pattern using the first pattern bynonlinear processing steps comprises: anisotropically etching thecrystalline substrate to form a first pattern in the crystallinesubstrate; removing the protective layer; and anisotropically etchingthe crystalline substrate to form a second pattern in the crystallinesubstrate having a second pitch p₂=p/2 along the first direction of thecrystalline substrate.
 7. The method of claim 1, further comprising:removing the top resist layer and the lower resist layer, therebyleaving the one or more of the metal layer and the dielectric layer asthe second pattern over the substrate; and etching the substrate totransfer the second pattern to the substrate.
 8. The method of claim 1,wherein shadow evaporating at least one of the metal layer or thedielectric layer comprises depositing the at least one of the metallayer or the dielectric layer over the substrate at a first side of thelower resist layer and then depositing the at least one of a metal layeror the dielectric layer over the substrate at a second side of the lowerresist layer.
 9. The method of claim 1, wherein the film stack comprisesa resist layer disposed on a sacrificial layer.
 10. The method of claim9, wherein the step of forming a second pattern using the first patternby nonlinear processing steps comprises: etching the sacrificial layerto form a patterned sacrificial layer; forming a conformal layer on thepatterned sacrificial layer, wherein a sidewall thickness of theconformal layer is about p/4; depositing a polymer layer over theconformal layer such that spaces between the conformal layer are filled;etching a portion of the polymer layer and a top portion of theconformal layer to expose a top portion of the patterned sacrificiallayer; and removing the remaining polymer layer and the patternedsacrificial layer such that the remaining conformal layer forms a secondpattern having a pitch of p/2.
 11. The method of claim 1, wherein thestep of forming a film stack over a substrate comprises: forming asacrificial layer over an etch stop layer; and forming a resist layerover the sacrificial layer.
 12. The method of claim 11, wherein the stepof forming a second pattern using the first pattern by nonlinearprocessing steps comprises: etching the sacrificial layer to form the apatterned sacrificial layer, wherein the first pattern has a line widthof about p/4; forming a conformal layer on the patterned sacrificiallayer, wherein a sidewall thickness of the conformal layer is about p/4;etching a portion of the conformal layer to expose a top surface of thesacrificial layer and to expose a portion of the etch stop layer betweenthe patterned sacrificial layer; and removing the patterned sacrificiallayer to form a frequency doubled conformal layer.
 13. The method ofclaim 1, wherein the step of forming a film stack over a substratecomprises: forming a lower layer comprising one or more of ananti-reflective coating and a nitride over a substrate; and forming atop layer comprising one or more of a polymer and a photoresist over thelower layer.
 14. The method of claim 13, wherein the formation of thefirst pattern comprises: forming a plurality of “T” structures disposedon the substrate, wherein the “T” structure comprises a lower layerhaving a first thickness of h and a width of about p/4, and a top layerhaving a thickness of less than h and a width of about 3p/4, wherein pis a pitch of a lithographic exposure.
 15. The method of claim 13,wherein the step of forming a second pattern using the first pattern bynonlinear processing steps comprises: depositing a hard mask materialvertically over the substrate such that the hard mask material forms afirst pattern having a period of p; removing the top layer; etching thesubstrate thereby forming a second pattern having a pitch of p/2; andremoving the lower layer and the hard mask material.
 16. The method forself-aligned spatial frequency doubling comprising: forming a film stackover substrate such that the film stack comprises a first pattern havinga first pitch p formed by an optical exposure, the first pitch p beingat least smaller than twice the bandpass limit for the optical exposure,wherein the formation of the first pattern comprises: forming aplurality of T-shaped structures over the substrate; wherein eachT-shaped structure comprises a top layer formed over a lower layer, thelower layer having a thickness of h and a width of about p/4 and the toplayer having a thickness of less than h and a width of about 3p/4; andforming a second pattern using the first pattern by one or morenonlinear processing steps to provide the second pattern with a secondpitch p₂=p/2; wherein the formation of the second pattern comprises:planarizing the plurality of T-shaped structures with a polymer byfilling gaps over the substrate between adjacent T-shaped structureswith the polymer, anisotropically etching the polymer through the gapsover the substrate using the top layer of each T-shaped structure as anetching hard mask, removing the top layer and the lower layer of eachT-shaped structure, thereby leaving the etched polymer over thesubstrate as the second pattern having a pitch of p/2.
 17. The method ofclaim 16, wherein the lower layer comprises one or more of a polymer anda photoresist.
 18. The method of claim 16, wherein the second pattern isformed over the substrate and transferred to the substrate.
 19. Themethod of claim 16, wherein the step of forming a film stack over asubstrate comprises forming a protective layer over a crystallinesubstrate.
 20. The method of claim 19, wherein the first pattern havingthe first pitch p is along a first direction of the crystallinesubstrate.
 21. The method of claim 16, wherein the film stack comprisesa resist layer disposed on a sacrificial layer.
 22. The method of claim21, wherein the step of forming a second pattern using the first patternby one or more nonlinear processing steps comprises: etching thesacrificial layer to form a patterned sacrificial layer; forming aconformal layer on the patterned sacrificial layer, wherein a sidewallthickness of the conformal layer is about p/4; depositing a polymerlayer over the conformal layer such that spaces between the conformallayer are filled; etching a portion of the polymer layer and a topportion of the conformal layer to expose a top portion of the patternedsacrificial layer; and removing the remaining polymer layer and thepatterned sacrificial layer such that the remaining conformal layerforms the second pattern having a pitch of p/2.
 23. The method of claim16, wherein the step of forming a film stack over a substrate comprises:forming a sacrificial layer over an etch stop layer, and forming aresist layer over the sacrificial layer.
 24. The method of claim 23,wherein the step of forming a second pattern using the first pattern byone or more nonlinear processing steps comprises: etching thesacrificial layer to form the patterned sacrificial layer, wherein thefirst pattern has a line width of about p/4; forming a conformal layeron the patterned sacrificial layer, wherein a sidewall thickness of theconformal layer is about p/4; etching a portion of the conformal layerto expose a top surface of the sacrificial layer and to expose a portionof the etch stop layer between the patterned sacrificial layer; andremoving the patterned sacrificial layer to form a frequency doubledconformal layer.
 25. The method of claim 16, wherein the step of forminga film stack over a substrate comprises: forming a lower layercomprising one or more of an anti-reflective coating and a nitride overthe substrate; and forming a top layer comprising one or more of apolymer and a photoresist over the lower layer.
 26. The method of claim25, wherein the formation of the first pattern comprises: forming aplurality of “T” structures on the substrate, wherein the “T” structurecomprises a lower layer having a first thickness of h and a width ofabout p/4, and a top layer having a thickness of less than h and a widthof about 3p/4, wherein p is a pitch of a lithographic exposure.
 27. Themethod of claim 25, wherein the step of forming a second pattern usingthe first pattern by one or more nonlinear processing steps comprises:depositing a hard mask material vertically over the substrate such thatthe hard mask material forms a first pattern having a period of p;removing the top layer; etching the substrate thereby forming a secondpattern having a pitch of p/2; and removing the lower layer and the hardmask material.